primepca
Matthew Stephens
2019-10-05
Last updated: 2019-10-20
Checks: 7 0
Knit directory: misc/analysis/
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Introduction
I briefly experiment with primePCA package for PCA with missing data and compare its results with those from softImpute. To make the two comparable I run both with no centering (set center=FALSE in primePCA).
library("primePCA")
library("softImpute")Loading required package: MatrixLoaded softImpute 1.4This first try is 50% missingness in every row, a rank 1 matrix:
set.seed(123)
n = 100
p = 200
missprob = rep(0.5,100) #make every row have 50% missing
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)
for(i in 1:n){
for(j in 1:p){
if(runif(1)<missprob[i]){X[i,j]=NA}
}
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)Convergence threshold is hit.res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=1,col=2)
This is the same but missingness varies by row (uniform on 0,1).
set.seed(123)
n = 100
p = 200
missprob = runif(n) #
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)
for(i in 1:n){
for(j in 1:p){
if(runif(1)<missprob[i]){X[i,j]=NA}
}
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)Convergence threshold is hit.res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=-1,col=2)
This example has higher missingness (0.8,1)
set.seed(123)
n = 100
p = 200
missprob = 0.8+ 0.2*runif(n) #at least 80% missing
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)
for(i in 1:n){
for(j in 1:p){
if(runif(1)<missprob[i]){X[i,j]=NA}
}
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)Max iteration number is hit.res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=-1,col=2)
cor(cbind(v,res.p$V_cur,res.s$v)) v
v 1.0000000 -0.9011763 0.9083774
-0.9011763 1.0000000 -0.9911967
0.9083774 -0.9911967 1.0000000…and higher missingness again, (0.9,1). (I increased n so that every column has sufficient non-missing entries):
set.seed(123)
n = 1000
p = 200
missprob = 0.9+ 0.1*runif(n) #at least 90% missing
u = rnorm(n)
v = rnorm(p)
X = u %*% t(v) + rnorm(n*p)
for(i in 1:n){
for(j in 1:p){
if(runif(1)<missprob[i]){X[i,j]=NA}
}
}
res.p = primePCA(X, 1,trace.it=FALSE,center=FALSE)Max iteration number is hit.res.s = softImpute(X,1)
plot(res.s$v,res.p$V_cur,main="v from primePCA vs softimpute")
abline(a=0,b=-1,col=2)
cor(cbind(v,res.p$V_cur,res.s$v)) v
v 1.0000000 0.9878358 -0.9867028
0.9878358 1.0000000 -0.9983583
-0.9867028 -0.9983583 1.0000000Interestingly, the results from trace.it=FALSE in primePCA suggest it is maybe entering an infinite loop in this case. I guess that maybe this is probably because of changes in the rows selected, and indeed was able to avoid it by setting very large thresh_sigma=1e100. (In this case it appears to just filter out the rows with only one entry; in the other case it sometimes filters out one additional row).
sessionInfo()R version 3.6.0 (2019-04-26)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Mojave 10.14.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] softImpute_1.4 Matrix_1.2-17 primePCA_1.0
loaded via a namespace (and not attached):
[1] workflowr_1.4.0 Rcpp_1.0.2 lattice_0.20-38 digest_0.6.20
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[9] git2r_0.26.1 magrittr_1.5 evaluate_0.14 stringi_1.4.3
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[21] compiler_3.6.0 htmltools_0.3.6 knitr_1.23